Theorem D.1 (Theorems 15.10 in [1]}) 

Suppose \(p(v)\)  is a trivariate polynomial with B-form \(p(v)=\sum _{i+j+k+l=d} \gamma _{ijkl}B_{ijkl}^{d}(v)\) . Define \(\gamma _{ijkl}^{(0)}:=\gamma _{ijkl}\) , \(i+j+k+l=d\) . Suppose \(v\)  has barycentric coordinates \(b=(b_1,b_2,b_3,b_4)\) . Then
\(p(v)=\sum _{i+j+k+l=d-m} \gamma _{ijkl}^{(m)}B_{ijkl}^{d-m}(v),\) 
